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Physical Review A

Stability of a Bose-Einstein condensate in an anharmonic trap

Barnali Chakrabarti, Tapan Kumar Das, Pankaj Kumar Debnath

Published May 18, 2009• 23 citations
Publisher

Abstract

We study the stability of Bose-Einstein condensate (BEC) with repulsive and attractive interatomic interactions in a harmonic plus quartic trap $[V(r)=\frac{1}{2}m{\ensuremath{\omega}}^{2}{r}^{2}+\ensuremath{\lambda}{r}^{4}]$. We find that BEC with repulsive interaction becomes more stable for $\ensuremath{\lambda}>0$. For $\ensuremath{\lambda}<0$, we observe a different metastability of the condensate even when the scattering length is positive. For BEC with attractive interaction, we observe dramatic change in the stability factor $\frac{{A}_{\text{cr}}|{a}_{\text{sc}}|}{{a}_{\text{ho}}}$ due to the anharmonicity. The frequencies of the collective excitations are also modified by the atomic interaction and by the anharmonicity.

DOI
10.1103/physreva.79.053629

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We study the stability of Bose-Einstein condensate (BEC) with repulsive and attractive interatomic interactions in a harmonic plus quartic trap [V(r)=12m\ensuremathω2r2+\ensuremathλr4][V(r)=\frac{1}{2}m{\ensuremath{\omega}}^{2}{r}^{2}+\ensuremath{\lambda}{r}^{4}][V(r)=21​m\ensuremathω2r2+\ensuremathλr4]. We find that BEC with repulsive interaction becomes more stable for \ensuremathλ>0\ensuremath{\lambda}>0\ensuremathλ>0. For \ensuremathλ<0\ensuremath{\lambda}<0\ensuremathλ<0, we observe a different metastability of the condensate even when the scattering length is positive. For BEC with attractive interaction, we observe dramatic change in the stability factor Acr∣asc∣aho\frac{{A}_{\text{cr}}|{a}_{\text{sc}}|}{{a}_{\text{ho}}}aho​Acr​∣asc​∣​ due to the anharmonicity. The frequencies of the collective excitations are also modified by the atomic interaction and by the anharmonicity.
We study the instability of collective excitations of a three-dimensional Bose-Einstein condensate with repulsive and attractive interactions in a shallow trap designed as a quadratic plus a quartic potential. By using a correlated many-body theory, we determine the excitation modes and probe the critical behavior of collective modes, having a crucial dependence on the anharmonic parameter. We examine the power-law behavior of monopole frequency near criticality. In Gross-Pitaevskii variational treatment [Phys. Rev. Lett. 80, 1576 (1998)] the power-law exponent is determined as one-fourth power of $(1\ensuremath{-}\frac{A}{{A}_{\mathit{cr}}})$, AAA is the number of condensate atoms and Acr{A}_{\mathit{cr}}Acr​ is the critical number near collapse. We observe that the power-law exponent becomes 16\frac{1}{6}61​ in our calculation for the pure harmonic trap and it becomes 17\frac{1}{7}71​, for traps with a small anharmonic distortion. However for large anharmonicity the power law breaks down.
The stability and collective excitation of Bose–Einstein condensates with both two- and three-body interactions in a two-dimensional anharmonic trap (i.e., harmonic plus quartic trap) are investigated. By using the variational method, the influence of the three-body interaction and the anharmonicity on the stability are discussed in detail. It is found that the anharmonicity of the trap and the three-body interaction have significant effect on the stability and collective excitations of the system.
The dynamics of weakly interacting three-dimensional Bose-Einstein condensates (BECs), trapped in external axially symmetric plus anharmonic distortion potential are studied. Within a variational approach and time-dependent Gross-Pitaevskii equation, the coupled condensate width equations are derived. By modulating anharmonic distortion of the trapping potential, nonlinear features are studied numerically and illustrated analytically, such as mode coupling of oscillation modes, and resonances. Furthermore, the stability of attractive interaction BEC in both repulsive and attractive anharmonic distortion is examined. We demonstrate that a small repulsive and attractive anharmonic distortion is effective in reducing (extending) the condensate stability region since it decreases (increases) the critical number of atoms in the trapping potential.
It is investigated that the collective excitations of a one-dimensional Bose-Einstein condensate(BEC) with repulsive interaction between atoms in a quadratic plus quartic trap V(x)=12(x~2+λx~4).By using the variational approach,the analytical expressions are derived for two low-energy collective modes,and the effect of the anharmonicity of the potential trap on BEC collective excitations is studied.When(λ0) the frequencies will be blue shifted and when λ0 the frequencies will be red shifted.Meanwhile,the variations of the center-of-mass of the condensate and its width under different values of the driving amplitude are discussed.It is found that the two modes couple each other due to the anharmonicity,and the beating structure for the variation of the width occur.Finally,the response result corresponding to the frequency driving is given.
The zero-temperature ground state properties of experimental 87Rb condensate are studied in a harmonic plus quartic trap [ V(r) = ½mω2r2 + λr4 ]. The anharmonic parameter (λ) is slowly tuned from harmonic to anharmonic. For each choice of λ, the many-particle Schrödinger equation is solved using the potential harmonic expansion method and determines the lowest effective many-body potential. We utilize the correlated two-body basis function, which keeps all possible two-body correlations. The use of van der Waals interaction gives realistic pictures. We calculate kinetic energy, trapping potential energy, interaction energy, and total ground state energy of the condensate in this confining potential, modelled experimentally. The motivation of the present study is to investigate the crucial dependency of the properties of an interacting quantum many-body system on λ. The average size of the condensate has also been calculated to observe how the stability of repulsive condensate depends on anharmonicity. In particular, our calculation presents a clear physical picture of the repulsive condensate in an anharmonic trap.
We investigate the collective excitations of a one-dimensional Bose-Einstein condensate with repulsive interaction between atoms in a quadratic plus quartic trap. Using variational approaches, the coupled equations of motions for the center-of-mass coordinate of the condensate and its width are derived. Then, two low-energy excitation modes are obtained analytically. The frequency shift induced by the anharmonic distortion, and the collapse and revival of the collective excitations originating from the nonlinear coupling between the two modes, are discussed.